Abstract: This DFG-funded project aims to model astrophysical objects physically consistent for lifelike and fast 3D visualization. Therefore, methods and algorithms are developed to reconstruct the spatial structure of various objects from astronomical observations and physical constraints to visualize them interactively with modern, high-resolution planetarium displays. Cosmological effects are visualized based on scientific facts in an accessible manner for the public.

Abstract: We present a novel method to compute anisotropic
shading for direct volume rendering to improve the perception of the
orientation and shape of surface-like structures. We determine the
scale-aware anisotropy of a shading point by analyzing its ambient region.
We sample adjacent points with similar scalar values to perform a principal
component analysis by computing the eigenvectors and eigenvalues of the
covariance matrix. In particular, we estimate the tangent directions, which
serve as the tangent frame for anisotropic bidirectional reflectance
distribution functions. Moreover, we exploit the ratio of the eigenvalues to
measure the magnitude of the anisotropy at each shading point. Altogether,
this allows us to model a data-driven, smooth transition from isotropic to
strongly anisotropic volume shading. In this way, the shape of volumetric
features can be enhanced significantly by aligning specular highlights along
the principal direction of anisotropy. Our algorithm is independent of the
transfer function, which allows us to compute all shading parameters once
and store them with the data set. We integrated our method in a GPU-based
volume renderer, which offers interactive control of the transfer function,
light source positions, and viewpoint. Our results demonstrate the benefit
of anisotropic shading for visualization to achieve data-driven local
illumination for improved perception compared to isotropic shading.

Abstract: Inspired by vector field topology, an established tool
for the extraction and identification of important features of flows and
vector fields, we develop means for the analysis of the structure of light
transport. For that, we derive an analogy to vector field topology that
defines coherent structures in light transport. We also introduce
Finite-Time Path Deflection (FTPD), a scalar quantity that represents the
deflection characteristic of all light transport paths passing through a
given point in space. For virtual scenes, the FTPD can be computed directly
using path-space Monte Carlo integration. We visualize the FTPD field for
several example scenes and discuss the revealed structures. Lastly, we show
that the coherent regions visualized by the FTPD are closely related to the
coherent regions in our new topologically-motivated analysis of light
transport. FTPD visualizations are thus also visualizations of the structure
of light transport.

Abstract: We present a novel and efficient method to compute
volumetric soft shadows for interactive direct volume visualization to
improve the perception of spatial depth. By direct control of the softness
of volumetric shadows, disturbing visual patterns due to hard shadows can be
avoided and users can adapt the illumination to their personal and
application-specific requirements. We compute the shadowing of a point in
the data set by employing spatial filtering of the optical depth over a
finite area patch pointing toward each light source. Conceptually, the area
patch spans a volumetric region that is sampled with shadow rays; afterward,
the resulting optical depth values are convolved with a low-pass filter on
the patch. In the numerical computation, however, to avoid expensive shadow
ray marching, we show how to align and set up summed area tables for both
directional and point light sources. Once computed, the summed area tables
enable efficient evaluation of soft shadows for each point in constant time
without shadow ray marching and the softness of the shadows can be
controlled interactively. We integrated our method in a GPU-based volume
renderer with ray casting from the camera, which offers interactive control
of the transfer function, light source positions, and viewpoint, for both
static and time-dependent data sets. Our results demonstrate the benefit of
soft shadows for visualization to achieve user-controlled illumination with
many-point lighting setups for improved perception combined with high
rendering speed.

Abstract: We introduce a refractive radiative transfer equation
to the graphics community for the physically based rendering of
participating media that have a spatially varying index of refraction. We
review principles of geometric non-linear optics that are crucial to discuss
a more generic light transport equation. In particular, we present an
optical model that has an integral form suitable for rendering. We show
rigorously that the continuous bending of light rays leads to a
non-linear scaling of radiance. To obtain physically correct results, we
build on the concept of basic radiance—known
from discontinuous refraction—to conserve energy in such complex media. Furthermore, the generic model
accounts for the reduction in the speed of light due to the index of
refraction to render transient effects like the propagation of light echoes.
We solve the refractive volume rendering equation by extending photon
mapping with transient light transport in a refractive, participating
medium. We demonstrate the impact of our approach on the correctness of
rendered images of media that are dominated by spatially continuous
refraction and multiple scattering. Furthermore, our model enables us to
render visual effects like the propagation of light echoes or time-of-flight
imagery that cannot be produced with previous approaches.

Abstract: We present ambient scattering as a preintegration
method for scattering on mesoscopic scales in direct volume rendering.
Far-range scattering effects usually provide negligible contributions to a
given location due to the exponential attenuation with increasing distance.
This motivates our approach to preintegrating multiple scattering within a
finite spherical region around any given sample point. To this end, we solve
the full light transport with a Monte-Carlo simulation within a set of
spherical regions, where each region may have different material parameters
regarding anisotropy and extinction. This precomputation is independent of
the data set and the transfer function, and results in a small
preintegration table. During rendering, the look-up table is accessed for
each ray sample point with respect to the viewing direction, phase function,
and material properties in the spherical neighborhood of the sample. Our
rendering technique is efficient and versatile because it readily fits in
existing ray marching algorithms and can be combined with local illumination
and volumetric ambient occlusion. It provides interactive volumetric
scattering and soft shadows, with interactive control of the transfer
function, anisotropy parameter of the phase function, lighting conditions,
and viewpoint. A GPU implementation demonstrates the benefits of ambient
scattering for the visualization of different types of data sets, with
respect to spatial perception, high-quality illumination, translucency, and
rendering speed.

Abstract: The visualization of large data is a computationally
demanding task. The increase in performance and the flexible programmability
have made graphics processing units (GPUs) an attractive platform to address
large data visualization. The parallel architecture of GPUs and the low
costs, coupled with high availability, have paved the way for this
significant field of research. In this chapter, we review the fundamental
principles of modern graphics hardware briefly before we summarize the
latest research in GPU-based visualization techniques for stand-alone and
cluster-based systems.

Abstract: We present a spectral analysis of higher-order texture
advection in combination with Back and Forth Error Compensation and
Correction (BFECC). Semi-Lagrangian techniques exhibit high numerical
diffusion, which acts as a low-pass filter and tends to smooth out high
frequencies. In the spatial domain, numerical diffusion leads to a loss of
details and causes a blurred image. To reduce this effect, higher-order
interpolation methods or BFECC can be employed separately. In this paper, we
present a combination of both approaches and we analyze the quality of
different compositions of higher-order interpolation schemes with and
without BFECC. We employ radial power spectrum diagrams for different
advection times and input textures to evaluate the conservation of the
spectrum up to fifth-order polynomials. Our evaluation shows that the
results of texture advection are improved by using higher-order
interpolation.

Abstract: The 3D visualization of astronomical nebulae is a
challenging problem since only a single 2D projection is observable from our
fixed vantage point on Earth. We attempt to generate plausible and realistic
looking volumetric visualizations via a tomographic approach that exploits
the spherical or axial symmetry prevalent in some relevant types of nebulae.
Different types of symmetry can be implemented by using different randomized
distributions of virtual cameras. Our approach is based on an iterative
compressed sensing reconstruction algorithm that we extend with support for
position-dependent volumetric regularization and linear equality
constraints. We present a distributed multi-GPU implementation that is
capable of reconstructing high-resolution datasets from arbitrary
projections. Its robustness and scalability are demonstrated for
astronomical imagery from the Hubble Space Telescope. The resulting
volumetric data is visualized using direct volume rendering. Compared to
previous approaches, our method preserves a much higher amount of detail and
visual variety in the 3D visualization, especially for objects with only
approximate symmetry.

Abstract: Interactive visualization and simulation of
astrophysical phenomena enable digital planetariums and television
documentaries to take their spectators on a journey into deep space and
explore the astronomical wonders of our universe in 3D.

Abstract: This paper presents a new general-relativistic ray
tracer that enables image synthesis on an interactive basis by exploiting
the performance of graphics processing units (GPUs). The application is
capable of visualizing the distortion of the stellar background as well
as trajectories of moving astronomical objects orbiting a compact mass. Its
source code includes metric definitions for the Schwarzschild and Kerr
spacetimes that can be easily extended to other metric definitions, relying
on its object-oriented design. The basic functionality features a scene
description interface based on the scripting language Lua, real-time image
output, and the ability to edit almost every parameter at runtime. The
ray tracing code itself is implemented for parallel execution on the GPU
using NVidia’s Compute Unified Device Architecture (CUDA), which leads to
performance improvement of an order of magnitude compared to a single CPU
and makes the application competitive with small CPU cluster architectures.

Abstract: We present an exemplary steering system that performs
2D flow simulation and visualization on graphics processing units (GPUs).
The topology of a vector field provides the overall structure and therefore
lends itself for steering purposes. We build on the concept of Lagrangian
coherent structures present as ridges in the finite-time Lyapunov exponent
(FTLE). This allows to perform steering with respect to the true
time-dependent dynamics in a given time scope. Based on the insights from
the FTLE visualization, our CUDA-based implementation allows effective
interactive manipulation of boundary conditions such as solid obstacles or
velocity profiles.

Abstract: Sort first distributions have been studied and used far less than sort last distributions for parallel volume rendering, especially
when the data is too large to be replicated fully. We demonstrate that sort first distributions are not only a viable method of performing
data scalable parallel volume rendering, but more importantly they allow for a range of rendering algorithms and techniques that are
not efficient with sort last distributions. Several of these algorithms are discussed and two of them are implemented in a parallel
environment: a new improved variant of early ray termination to speed up rendering when volumetric occlusion occurs and a volumetric
shadowing technique that produces more realistic and informative images based on half angle slicing. Improved methods of distributing
the computation of the load balancing and loading portions of a subdivided data set are also presented. Our detailed test results for
a typical GPU cluster with distributed memory show that our sort first rendering algorithm outperforms sort last rendering in many
scenarios.

Abstract: We extend direct volume rendering with a unified model for generalized isosurfaces, also called interval volumes, allowing a wider
spectrum of visual classification. We generalize the concept of scale-invariant opacity—typical for isosurface rendering—to semi-transparent
interval volumes. Scale-invariant rendering is independent of physical space dimensions and therefore directly facilitates the analysis of
data characteristics. Our model represents sharp isosurfaces as limits of interval volumes and combines them with features of direct volume
rendering. Our objective is accurate rendering, guaranteeing that all isosurfaces and interval volumes are visualized in a crack-free way with
correct spatial ordering. We achieve simultaneous direct and interval volume rendering by extending preintegration and explicit peak finding
with data-driven splitting of ray integration and hybrid computation in physical and data domains. Our algorithm is suitable for efficient parallel
processing for interactive applications as demonstrated by our CUDA implementation.

A Parallel Preconditioned Conjugate Gradient Solver for the Poisson Problem
on a Multi-GPU Platform

Abstract: We present a parallel conjugate gradient solver for the Poisson problem optimized for multi-GPU platforms. Our
approach includes a novel heuristic Poisson preconditioner which is well-suited for massively-parallel SIMD processing. Furthermore, we address the problem of limited transfer rates over typical data channels such as the PCI-express bus relative to the bandwidth requirements of powerful GPUs. Specifically, naïve communication schemes can severely reduce the achievable
speedup in such communication-intense algorithms. For this reason,
we employ overlapping memory transfers to establish a high
level of concurrency and to improve scalability. We have implemented
our model on a high-performance workstation with multiple
hardware accelerators. We will discuss the mathematical
principles, give implementation details, and present the performance
and the scalability of the system.

Abstract: We present a physically-based fluid simulation with dynamic grid refinement on parallel SIMD graphics hardware. The irregular and dynamic structure of an adaptive grid requires sophisticated memory access patterns as well as a decomposition of the problem for parallel processing and the distribution of tasks to multiple threads. In this paper, we focus on the representation and management of the dynamic grid on the graphics device for an efficient parallelization of the advection step and the iterative solving of the Poisson equation. In order to achieve high performance, we utilize the hardware’s capabilities like fast cache access and trilinear filtering. Furthermore, expensive data transfer between host and device is minimized to avoid a major bottleneck. We report results on the inherent overhead of the dynamic grid compared to an equivalent Cartesian grid. In addition, a visual simulation of smoke is presented with radiosity-based illumination and volume ray casting at interactive frame rates.

2008

Hardware
Accelerated Fluid
Dynamics with Adaptive Grid Refinement

M. AmentWSI/GRIS, University of
Tübingen,
Diploma Thesis, 2008.

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Abstract: In this thesis, a physically-based fluid simulation with dynamic grid refinement parallel SIMD graphics hardware is presented. The irregular and dynamic structure of an adaptive grid requires sophisticated memory access patterns as well as a decomposition of the problem for parallel processing and the distribution of tasks to multiple threads. The focus of this thesis lies on the representation and management of the dynamic grid on the graphics device for an efficient parallelization of the advection step and the iterative solving of the Poisson equation. In order to achieve high performance, the hardware's capabilities like fast cache access and trilinear filtering are utilized. Furthermore, expensive data transfer between host and device is minimized to avoid a major bottleneck. Results on the inherent overhead of the dynamic grid compared to an equivalent Cartesian grid are reported. In addition, a visual simulation of smoke is presented with radiosity-based illumination and volume ray casting at interactive frame rates.